Connections by bundles of optical fibres are intended to replace numerous transmissions of signals, commands or data at present effected by electrical cables. To allow the time-division multiplexing of exchanges of information between the central control unit and the peripheral units, it is necessary to have branching elements, or branchers, for dividing the luminous energy emanating from a transmitting bundle between two receiving bundles. Associated in cascade, branchers of this type, by successive divisions, enable the optical energy to be distributed between the various peripheral units, thus authorising a transmission structure known by the name of "busbar". Depending upon the branching configuration adopted, the brancher has to be designed to divide the radiation received into two equal or unequal parts (one quarter and three quarters or one eighth and seven eighths for example). In every case, it is required to have minimal insertion losses for limiting the attenuation of the signal transmitted. In addition, to ensure that the branching of the optical energy is unaffected by possible fibre breakages in the transmitting bundle, the luminous fluxes conveyed by the various fibres have to be carefully mixed in the brancher before the luminous energy is divided.